Explanation

Optimal patterns are optimal for detection. To see this, imagine you receive only m < n pulses of the package of n sent out. The detection process consists of reconstructing the detection pattern around the m points, and next finding the shift from the pattern sent out to the reconstructed one in the time, frequence grid. Once the former action is carried out, the latter one is straightforward.

Suppose there were two ways of completing the m points to the original detection pattern. Then the two ways would represent an overlap of m points. The restriction on the overlap (being 1) sees to it that m 1. Hence, if we receive at least two points from a package, it determines a unique time, frequency shift.